The trains have ample room for big bags, but sometimes the space can be quite a ways from your seat or out of your sight. Take a minute and maybe buckle the straps to posts or something, or buckle the two bags together. Anything to slow somebody down who might "accidentally" pick up your bag.

I second (third, whatever) the advice to take the train here. You will see a little of the country, can get up and stretch enroute, and going from city center to city center is lots more convenient than getting to and from outlying airports.

And the bus option could work very nicely too.

Romelle